The change in the number of phase transitions for perturbations of finite range interactions is studied. A Monte-Carlo simulation was performed for a translation invariant spin 1/2 ferromagnetic model in Z² with fundamental bonds A = {(0,0);(0,1)} B = {(0,0);(2,0)} C = {(0,0);(0,1);(1,1);(1,0)} The model exhibits one phase transition if the coupling constant J(A) is zero, but two phase transitions were found when J(A) is non zero and small enough. The generalization of this situation is provided by a construction, due to J. Slawny, which through a sequence of progressively smaller perturbations yields models with an arbitrary minimum number of phase transitions. However, such construction requires the existence of interactions with one fundamental bond such that for all values of the coupling constants the Gibbs state is unique even when the interaction is perturbed by an arbitrary finite range perturbation of small enough norm. In this work it is proven that such property is exhibited by some translation invariant systems in Z^ν with finite state space at each point. The proof applies to models with real interactions and whose fundamental bonds are all multiple of a single bond which is of prime order and which is obtained as the product—in the group ring structure of the dual space—of one dimensional bonds whose non trivial projections at each lattice site are unique. The proof is based on the Dobrushin-Pecherski criterion concerning the uniqueness of Gibbs states under perturbations. Such criterion is restated so that only transition functions on sets of simple geometry are involved. In addition, an algebraic characterization is presented for the set of Gibbs states for ferromagnetic systems for which the state space at each lattice site is a compact abelian group. This is a generalization of the theory originally introduced by Slawny for spin 1/2 ferromagnetic models and later extended by Pfister to ferromagnetic models for which the state space at each point is a finite product of tori and finite abelian groups. / Ph. D.

A new physical and mathematical model for the epilepsies is proposed, based on the theory of bond percolation on finite lattices. Within this model, the onset of seizures in the brain is identified with the appearance of spanning clusters of neurons engaged in the spurious and uncontrollable electrical activity characteristic of seizures. It is proposed that the fraction of excitatory to inhibitory synapses can be identified with a bond probability, and that the bond probability is a randomly varying quantity displaying Gaussian statistics. The consequences of the proposed model to the treatment of the epilepsies is explored. The nature of the data on the epilepsies which can be acquired in a clinical setting is described. It is shown that such data can be analyzed to provide preliminary support for the bond percolation hypothesis, and to quantify the efficacy of anti-epileptic drugs in a treatment program. The results of a battery of statistical tests on seizure distributions are discussed. The physical theory of the electroencephalogram (EEG) is described, and extant models of the electrical activity measured by the EEG are discussed, with an emphasis on their physical behavior. A proposal is made to explain the difference between the power spectra of electrical activity measured with cranial probes and with the EEG. Statistical tests on the characteristic EEG manifestations of epileptic activity are conducted, and their results described. Computer simulations of a correlated bond percolating system are constructed. It is shown that the statistical properties of the results of such a simulation are strongly suggestive of the statistical properties of clinical data. The study finds no contradictions between the predictions of the bond percolation model and the observed properties of the available data. Suggestions are made for further research and for techniques based on the proposed model which may be used for tuning the effects of anti-epileptic drugs. / Ph. D.

In 1867, James Clerk Maxwell introduced a thought experiment involving a micro-scopic being (observer) capable of making precise measurements of microscopic quantitiesthrough observation of the micro-dynamics in a thermodynamic system. This observerlater became known as Maxwell’s demon due to its devious impact on thermodynamics,particularly the perceived violation of the second law. Subsequently, Leo Szilard pro-posed a machine, the so-called Szilard Machine, which, by utilising a Maxwell’s demon,successfully extracts work from thermal fluctuations in a closed system, seemingly vio-lating the second law. This thesis re-evaluates the second law of thermodynamics in the context of the Szi-lard Machine and Maxwell demons. The study explores the intersection of informationtheory and thermal physics, both theoretically and practically, with the aid of MonteCarlo simulations. The results indicate that machines with information feedback control,such as those utilising a Maxwell demon, challenge classical statements of the second lawof thermodynamics. This is because classical formulations, such as Clausius’ and Kelvin’sstatements, do not account for the entropic content of information. Simulations of thesefeedback processes, in conjunction with the detailed fluctuation theorem, provide a basisfor understanding feedback processes in so-called information machines. Ultimately, thesecond law of thermodynamics is upheld by an alternative statement endorsed by thedetailed fluctuation theorem.

Orientador: Mário Noboru Tamashiro / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-10-31T13:34:08Z (GMT). No. of bitstreams: 1 Oliveira_FranciscoOlivade_M.pdf: 8605584 bytes, checksum: 238f8b9df41bbaab50c51d355549ac7d (MD5) Previous issue date: 2016 / Resumo: Neste trabalho é realizada uma sintética revisão bibliográfica acerca do estudo de filmes monomoleculares na interface ar-água (filmes de Langmuir), seu desenvolvimento histórico e relação atual com tópicos avançados em física de membranas biológicas e biomiméticas, além das vantagens e desvantagens de algumas técnicas experimentais para caracterização de filmes de Langmuir. Visando a descrição de filmes de Langmuir formados por fosfolipídios, são discutidos alguns modelos teóricos como preâmbulo para a apresentação do modelo de gás de rede de Doniach (Doniach lattice gas: DLG), para o qual é apresentada a solução em aproximação de pares, implementada através de cálculos exatos na rede de Bethe. Por fim, os parâmetros do modelo em aproximação de pares são ajustados a dados experimentais obtidos de isotermas de compressão-expansão para dois fosfolipídios zwitteriônicos: o dimiristoilfosfatidilcolina (DMPC) e o dipalmitoilfosfatidilcolina (DPPC) / Abstract: In this work, we present a brief bibliographic review on the study of monomolecular films on the air-water interface (Langmuir films), their historical development and present relation with advanced subjects on biological and biomimetic membranes, besides the advantages and disadvantages of certain experimental techniques for the characterization of Langmuir films. In order to describe phospholipid Langmuir films, we discuss some theoretical models as a preamble to presenting the Doniach lattice gas (DLG) model, which we solve in the pair approximation, implemented through exact calculations on the Bethe lattice. Finally, we adjust the parameters of the model in the pair approximation to experimental data obtained from compression-expansion isotherms for two zwitterionic phospholipids: dimyristoylphosphatidylcholine (DMPC) and dipalmitoylphosphatidylcholine (DPPC) / Mestrado / Física / Mestre em Física / 1186359/2013 / CAPES

Thesis (PhD)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: In this dissertation we address the conservation of topological states in polymer knots. Topological constraints are frequently included into theoretical descriptions of polymer systems through invariants such as winding numbers and linking numbers of polynomial invariants. In contrast, our approach is based on sequences of manipulations of knots that maintain a given knot's topology; these are known as Reidemeister moves. We begin by discussing basic properties of knots and their representations. In particular, we show how the Reidemeister moves may be viewed as rules for dynamics of crossings in planar projections of knots. Thereafter we consider various combinatoric enumeration procedures for knot configurations that are equivalent under chosen topological constraints. Firstly, we study a reduced system where only the zeroth and first Reidemeister moves are allowed, and present a diagrammatic summation of all contributions to the associated partition function. The partition function is then calculated under basic simplifying assumptions for the Boltzmann weights associated with various configurations. Secondly, we present a combinatoric scheme for enumerating all topologically equivalent configurations of a polymer strand that is wound around a rod and closed. This system has the constraint of a fixed winding number, which may be viewed in terms of manipulations that obey a Reidemeister move of the second kind of the polymer relative to the rod. Again configurations are coupled to relevant statistical weights, and the partition function is approximated. This result is used to calculate various physical quantities for confined geometries. The work in that chapter is based on a recent publication, "Conservation of polymer winding states: a combinatoric approach", C.M. Rohwer, K.K. Müller-Nedebock, and F.-E. Mpiana Mulamba, J. Phys. A: Math. Theor. 47 (2014) 065001. The remainder of the dissertation is concerned with a dynamical description of the Reidemeister moves. We show how the rules for crossing dynamics may be addressed in an operator formalism for stochastic dynamics. Differential equations for densities and correlators for crossings on strands are calculated for some of the Reidemeister moves. These quantities are shown to encode the relevant dynamical constraints. Lastly we sketch some suggestions for the incorporation of themes in this dissertation into an algorithm for the simulated annealing of knots. / AFRIKAANSE OPSOMMING: In hierdie tesis ondersoek ons die behoud van topologiese toestande in knope. Topologiese dwangvoorwaardes word dikwels d.m.v. invariante soos windingsgetalle, skakelgetalle en polinomiese invariante in die teoretiese beskrywings van polimere ingebou. In teenstelling hiermee is ons benadering gebaseer op reekse knoopmanipulasies wat die topologie van 'n gegewe knoop behou - die sogenaamde Reidemeisterskuiwe. Ons begin met 'n bespreking van die basiese eienskappe van knope en hul daarstellings. Spesi ek toon ons dat die Reidemeisterskuiwe beskryf kan word i.t.v. reëls vir die dinamika van kruisings in planêre knoopprojeksies. Daarna beskou ons verskeie kombinatoriese prosedures om ekwivalente knoopkon gurasies te genereer onderhewig aan gegewe topologiese dwangvoorwaardes. Eerstens bestudeer ons 'n vereenvoudigde sisteem waar slegs die nulde en eerste Reidemeisterskuiwe toegelaat word, en lei dan 'n diagrammatiese sommasie van alle bydraes tot die geassosieerde toestandsfunksie af. Die partisiefunksie word dan bereken onderhewig aan sekere vereenvoudigende aannames vir die Boltzmanngewigte wat met die verskeie kon- gurasies geassosieer is. Tweedens stel ons 'n kombinatoriese skema voor om ekwivalente kon gurasies te genereer vir 'n polimeer wat om 'n staaf gedraai word. Die beperking tot 'n vaste windingsgetal in hierdie sisteem kan daargestel word i.t.v. 'n Reidemeister skuif van die polimeer t.o.v. die staaf. Weereens word kon gurasies gekoppel aan relevante statistiese gewigte en die partisiefunksie word benader. Verskeie siese hoeveelhede word dan bereken vir beperkte geometrie e. Die werk in di e hoofstuk is gebaseer op 'n onlangse publikasie, "Conservation of polymer winding states: a combinatoric approach", C.M. Rohwer, K.K. Müller-Nedebock, and F.-E. Mpiana Mulamba, J. Phys. A: Math. Theor. 47 (2014) 065001. Die res van die tesis handel oor 'n dinamiese beskrywing van die Reidemeisterskuiwe. Ons toon hoe die re els vir kruisingsdinamika beskryf kan word i.t.v. 'n operatorformalisme vir stochastiese dinamika. Di erensiaalvergelykings vir digthede en korrelatore vir kruisings op stringe word bereken vir sekere Reidemeisterskuiwe. Daar word getoon dat hierdie hoeveelhede die relevante dinamiese beperkings respekteer. Laastens maak ons 'n paar voorstelle vir hoe idees uit hierdie tesis geï nkorporeer kan word in 'n algoritme vir die gesimuleerde vereenvoudiging van knope.

Thesis (MSc (Physics))--University of Stellenbosch, 2005. / It was Wigner that in the 1950’s first introduced the idea of modelling physical reality with an ensemble of random matrices while studying the energy levels of heavy atomic nuclei. Since then, the field of Random Matrix Theory has grown tremendously, with applications ranging from fluctuations on the economic markets to M-theory. It is the purpose of this thesis to discuss the basic concepts of Random Matrix Theory, using the ensembles of random matrices originally introduced by Wigner, the Gaussian ensembles, as a starting point. As Random Matrix Theory is classically concerned with the statistical properties of levels sequences, we start with a brief introduction to the statistical analysis of a level sequence before getting to the introduction of the Gaussian ensembles. With the ensembles defined, we move on to the statistical properties that they predict. In the light of these predictions, a few of the classical applications of Random Matrix Theory are discussed, and as an example of some of the important concepts, the Anderson model of localization is investigated in some detail.

The physical properties of single crystals of samarium monosulfide exhibit a first order semiconductor-to-metal transition near 6.5 kbar. However, thin films of SmS show only a gradual change in their properties on applying pressure and this renders the technical utilization of the material difficult. Several mechanisms have been proposed as the cause of the smoothing of the transition. They include intrinsic stress, impurities, grain size, improper stoichiometry, and porosity, all of which can be traced to the physical vapor deposition techniques employed in preparing the films. In contrast, chemical vapor deposition was employed in this study because previous work had shown that it could minimize these detrimental modifications in thin films. A new CVD system was tested using a volatile organometallic as the samarium source and reacting it with H₂S. The deposited films contained considerable amounts of oxygen as evidenced by structure analysis, and the origin was traced to the samarium organometallic. The reaction of oxygen-free samarium tricyclopentadienyl with H₂S as well as chemical transport are suggested for deposition of stress-free SmS thin films in future work.

An active particle converts energy to motion. An active suspension is a population of active particles, typically microscale, that are immersed in a viscous and/or elastic medium. This thesis is about the statistics of active suspensions. Unlike a suspension at thermodynamic equilibrium, we show that an active suspension inherently has non-Gaussian fluctuations due to an interplay between self-driven constituents and microscopic physics. Consequently, the diffusion of a tracer in an active suspension is not Gaussian. Our results explain some experiments with active suspensions that contain either swimming microorganisms or molecular motors. We provide different models for the fluctuations in dilute active suspensions, ranging from phenomenological to exact. The fundamental ingredient of such non-Gaussian fluctuations is an ultraslow convergence to the central limit theorem caused by truncated power-laws. Without any truncation, there is an intimate relation to the generalized central limit theorem. We suggest similar effects occur in many other systems. These may be associated with probability distributions that appear to be exponential.

The purpose of this investigation is to make more detailed studies of transformations. Fourteen compounds have been examined by high temperature X-ray diffraction for this purpose. The investigations have been carried out in such a way as to reveal: 1. the existence of transformations, 2. the influence of polarizability on thermal expansion, 3. the anisotropy of expansion, and 4. the discontinuity of thermal expansion.

Since their discovery in the 1950's by Erdos and Renyi, network theory (the study of objects and their associations) has blossomed into a full-fledged branch of mathematics. Due to the network's flexibility, diverse scientific problems can be reformulated as networks and studied using a common set of tools. I define a network G = (V,E) composed of two parts: (i) the set of objects V, called nodes, and (ii) set of relationships (associations) E, called links, that connect objects in V. We can extend the classic network of nodes and links by describing the intensity of these associations with weights. More formally, weighted networks augment the classic network with a function f(e) from links to the real line, uncovering powerful ways to model real-world applications. This thesis studies new ways to construct robust micro powergrids, mine people's perceptions of causality on a social network, and proposes a new way to analyze crowdsourcing all in the context of the weighted network model. The current state of Earth's ecosystem and intensifying climate calls on scientists to find new ways to harvest clean affordable energy. A microgrid, or neighborhood-scale powergrid built using renewable energy sources attached to personal homes, suggest one way to ameliorate this energy crisis. We can study the stability (robustness) of such a small-scale system with weighted networks. A novel use of weighted networks and percolation theory guides the safe and efficient construction of power lines (links, E) connecting a small set of houses (nodes, V) to one another and weights each power line by the distance between houses. This new look at the robustness of microgrid structures calls into question the efficacy of the traditional utility. The next study uses the twitter social network to compare and contrast causal language from everyday conversation. Collecting a set of 1 million tweets, we find a set of words (unigrams), parts of speech, named entities, and sentiment signal the use of informal causal language. Breaking a problem difficult for a computer to solve into many parts and distributing these tasks to a group of humans to solve is called Crowdsourcing. My final project asks volunteers to 'reply' to questions asked of them and 'supply' novel questions for others to answer. I model this 'reply and supply' framework as a dynamic weighted network, proposing new theories about this network's behavior and how to steer it toward worthy goals. This thesis demonstrates novel uses of, enhances the current scientific literature on, and presents novel methodology for, weighted networks.